sql self join without equal operator on column - mysql

Question

Post the problem and SQL solution which works. My confusion is, when I am doing self join in the past, there is always some equal value (equal operator) in columns to join, but in below example, it seems self join could work without using equal operator? In my below example, using minus operator and >, no equal operator to specify which columns used to join.
Wondering if no equal operator, how did underlying self join works in my example?
Problem,
Given a Weather table, write a SQL query to find all dates' Ids with higher temperature compared to its previous (yesterday's) dates.
+---------+------------+------------------+
| Id(INT) | Date(DATE) | Temperature(INT) |
+---------+------------+------------------+
| 1 | 2015-01-01 | 10 |
| 2 | 2015-01-02 | 25 |
| 3 | 2015-01-03 | 20 |
| 4 | 2015-01-04 | 30 |
+---------+------------+------------------+
For example, return the following Ids for the above Weather table:
+----+
| Id |
+----+
| 2 |
| 4 |
+----+
SQL solution,
select W1.Id
from Weather W1, Weather W2
where TO_DAYS(W1.Date)-TO_DAYS(W2.Date) = 1 and W1.Temperature > W2.Temperature

Answer 1

Writing it using an ANSI join, since they're a standard part of SQL:
select W1.Id
from Weather W1
inner join
Weather W2
on TO_DAYS(W1.Date)-TO_DAYS(W2.Date) = 1 and
W1.Temperature > W2.Temperature
(Should produce an identical result set)
A join is just the process of matching up two sets of rows - you have a row source on the "left" and a row source on the "right" of the join. In trivial cases, these row sources are tables, but a join may also join the results of any previous joins as the row sources.
In theory, in the join, the result would be a cartesian product - every row on the left would be matched with every row on the right. If this is what you want, you can indicate this with CROSS JOIN.
Usually, however, we want to restrict the result of the join to less than the cartesian product of the rows. And we express those restrictions by writing an ON clause (or in the WHERE clause in your example using the old-style comma join).
The most common type of join is an equijoin, where one or more columns on each side are compared for equality. But that is by no means required. It can be any predicates that make sense. E.g. one form of join that I employ semi-regularly I described as a "triangle join" (by no means standard terminology) where every row is matched with every row that comes later:
SELECT
*
FROM
Table t1
left join
Table t2
on
t1.ID < t2.ID
And that's perfectly fine. The row with the lowest ID in Table will be matched with every other row in the table. The row with the highest ID value will not be matched with any other rows.

Answer 2

That's called an "implicit join" - I suggest, you read up on SQL JOIN, for example at https://en.wikipedia.org/wiki/Join_(SQL).
In short: The database looks for fitting JOIN columns without requiring you to explicitly specify them.